Seismic vibrators are commonly used to produce the source signals necessary in the geophysical exploration for hydrocarbons. In field use, seismic vibrators are excited with a pilot signal that is typically a wave train that varies in frequency, referred to as a sweep, and lasts several seconds. The excitation of the vibrator is typically adjusted by a feedback loop controlled by a ground force signal that is computed from signals measured by accelerometers on the base plate and on the reaction mass of the source.
In this application of seismic vibrators, seismograms are generated by cross correlating the data recorded at various receiver locations with the pilot signal. This cross-correlation step compresses the impulse response of the data from the several seconds associated with the sweep to a few tens of milliseconds and thereby better approximates the signal that would be recorded by an ideal impulsive source. This step is followed by standard seismic data processing steps, such as surface consistent statistical deconvolution, static corrections, noise filtering, bandpass filtering, and imaging.
Five categories of problems with conventional seismic vibrator technology have long been recognized in industry. First, the cross-correlation process results in a pulse with undesirable characteristics, including a widened main lobe and sidelobes that appear as oscillations on either side of the main lobe. Second, the output is mixed phase, as a result of combining the correlation process, which results in a zero phase wavelet, with the earth attenuation filter and recording instruments, which are minimum phase.
This leads to several problems. For example, correlated data, unlike impulsive-source data, do not have well-defined arrival times. In addition, such data are no longer causal. Other processing techniques, such as statistical or spiking deconvolution, assume that the data are causal and minimum phase, and for that reason the processing results may not be accurate. Third, the pilot signal used in the correlation is generally substantially different from the actual signal put into the ground. The actual signal contains harmonics and other nonlinearities arising from the mechanics of the vibrator and its coupling with the ground. Processing the data with the pilot signal does not allow those harmonics and nonlinearities to be removed, which therefore appear as noise in the processed data. Fourth, acquiring seismic data is expensive and a major cost is associated with the number of source stations that can be used. Traditional vibrator technologies record only one source station at a time. Methods that allow acquisition using multiple source stations simultaneously would speed acquisition and reduce costs. Fifth, to increase the energy put into the ground two or more vibrators are typically used at each source station. However, spacing limitations result in the multiple vibrators forming an array that can limit the high frequencies in the data and thereby reduce resolution. Elevation changes may also limit the ability to correct for time shifts, also referred to as static corrections, between the vibrators. As further described in the next several paragraphs, industry has focused a substantial amount of effort in attempting to overcome these limitations.
The U.S. patents issued to Trantham, U.S. Pat. No. 5,400,299 and Andersen, U.S. Pat. No. 5,347,494 disclose methods that principally address the first category of problems. The methods result in improved impulse wavelet shapes. Trantham's disclosure also provides a causal and minimum phase impulse after removal of the vibrator pilot signal. However, processing is done with the pilot, which is only an approximation of the signature imparted into the ground. Also, Trantham's approach preferably requires pre-whitening the signal, in which white noise is added, to stabilize a spectral division from which the vibrator signature deconvolution filter is generated. This step prevents numerical errors in the division, but also may cause phase distortions and adds a precursor to the processed seismic data.
Andersen's method involves the choice of a sweep power spectrum that leads to an impulse response with a simple shape and an optimum length after correlation. Unlike conventional sweeps, which start around 8 Hz, Andersen's sweep starts at frequencies near 1 Hz. The presence of these lower frequencies results in a more desirable wavelet. This solution, however, only addresses the first of the problems noted above. In addition, the use of high-resolution wavelets requires that the sweep rate changes rapidly with time and is not realizable with standard hydraulic vibrators.
U.S. Pat. No. 5,550,786 issued to Allen discloses a method that uses a measured accelerometer signal or signals, such as the ground force, from each vibrator and sweep in an inversion process instead of a correlation with a pilot signal. The measured signals are related to the actual signal imparted into the ground by a transfer function of minimum phase, which is obtained by the process of minimum phase statistical deconvolution, which is commonly used in processing land data. Steps include inversion (also referred to as spectral division), bandpass filtering, and spiking deconvolution. A model trace is processed to make a phase correction of the deconvolved data.
Allen addresses the first three shortcomings discussed above. However, Allen's method applies an inverse filter by the process of spectral division, and it is recognized that a problem with such inverse filters is that at frequencies where the measured signals are small, the filter will apply a large gain and amplify any recorded noise. If the signal is zero, then inversion will be unstable. The data can be pre-whitened by adding a small amount of constant noise to stabilize the inversion, but the added noise can distort the phase of the data. Because processing techniques such as spiking deconvolution assumes that input data are minimum phase, the output results may not be predictable when such distortion is present. Allen attempts to solve these problems by using bandpass filters to reduce the noise outside the vibrator sweep band, and by processing a model trace in order to be able to calculate a phase correction. As will be understood to those skilled in the art, a preferable method would avoid the use of bandpass filters and phase corrections by eliminating the need to pre-whiten the data.
U.S. Pat. Nos. 5,719,821 and 5,721,710 issued to Sallas et al. discuss a matrix inversion scheme to separate the outputs from individual vibrators. The number of sweeps can be equal to or greater than the number of vibrators. This method solves a set of linear equations, which includes the measured motions from each vibrator and each sweep, to determine an optimal filter for inversion and separation. Although Sallas addresses the shortcomings listed above, the problems with inversion and phase errors discussed above in relation to Allen remain unsolved. U.S. Pat. No. 6,161,076 issued to Barr et al (2000) is similar to the prior work of Allen and Trantham. Barr misstates that Allen is using a single accelerometer signal instead of the ground force signal, and claims the use of a filter to convert the data to short-duration wavelets, as did Trantham. It is understood in the art that this process is equivalent to inversion followed by a bandpass filter, and thus the problems noted above are unaddressed. Barr specifically discloses using the harmonics or non-linear distortion to construct a wavelet of equal or greater bandwidth than the sweep. This approach also involves retention of noise components that reduce the quality of the subsequently processed data. Finally, Barr discloses phase encoding the sweeps for multiple vibrators, and the use of a different set of separation filters for each sweep before stacking the outputs.
U.K. Patent 2,359,363 to Jeffryes (2000) restates the Sallas disclosures, but with the addition of a filter to remove harmonics from the data and from measured vibrator signatures. As noted, filters are undesirable, as they inadequately remove harmonics and other non-linearities and thus reduce the quality of subsequently processed data.
There is a need for a method whereby seismic vibrator data can be acquired and processed in a manner that accurately represents the data, which would be derived from an impulse source. The method should involve use of a deterministic deconvolution that derives from measured vibrator motions. The method should not require addition of white noise to stabilize the processing computations. The method should not require use of a post-processing bandpass filter to eliminate harmonics and noise. The method should retain the correct phase of the underlying data to ensure subsequent processing techniques produce accurate results. The method should be applicable to arrays of more than one vibrator and provide for the separation of data recorded from multiple vibrators simultaneously. The present invention addresses these needs.